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Modeling, simulation and experimental research of single chamber hydro pneumatic suspension

hydro pneumatic suspension technology began with the hydro pneumatic suspension invented by T. carpone in the 1960s. Compared with the traditional suspension (leaf spring type), it has the advantages of large unit energy storage ratio, nonlinear stiffness and damping, compact structure, convenient control and so on. It has been widely used in foreign engineering vehicles and special vehicles. Since the 1980s, the technology has been introduced into some engineering vehicles in China. 4.2 the parts of steel parts that are often twisted and easy to wear should be heat treated. Then some researchers in China began to study this technology and achieved some results. However, there are still the following problems: [1] [2] [3]

(1) when designing hydro pneumatic suspension, there is no simple calculation formula for engineering designers to choose and use in design and verification

(2) at present, most of the research work that has been carried out remains in theory, with more simulations and less experiments

(3) at present, the domestic research work is carried out for the hydro pneumatic suspension of a certain vehicle type (introduced), and there is a lack of basic and systematic research on hydro pneumatic suspension

in view of the above problems, it is timely and necessary to carry out theoretical analysis and Experimental Research on hydro pneumatic suspension technology. This paper takes the most basic single chamber hydro pneumatic separated hydro pneumatic suspension as the research object, and carries out theoretical modeling and Experimental Research on it, in order to reveal the basic characteristics of hydro pneumatic suspension

1 working principle of single chamber hydro pneumatic suspension

Figure 1 is the structural schematic diagram of single chamber hydro pneumatic separated hydro pneumatic suspension. Three cavities are formed inside the whole suspension cylinder, namely, the rod free cavity (cavity I) of the suspension cylinder; The suspension cylinder has a rod cavity (a cavity); The cavity formed by the inner wall of the piston rod - the central cavity. The piston rod and piston assembly 2 are provided with a one-way valve 3 and a damping hole 4 to connect the central chamber with chamber II. When the suspension is in the compression stroke (the piston rod moves upward), the oil in chamber I and the central chamber is compressed and moves in two directions. Part of the oil flows into chamber II through check valve 3 and damping hole 4. It is believed that the new company will still stand at the high point of the material industry in the future; Another part of the oil enters the accumulator, reducing the volume of the gas chamber and increasing the nitrogen pressure. In this process, because the check valve 3 and damping hole 4 simultaneously connect the central chamber with chamber II, the flow rate of oil flowing through the check valve 3 and damping hole 4 is low, and the oil damping force is relatively small. Therefore, the gas in the accumulator is compressed to produce an elastic effect to inhibit the upward movement of the piston rod, which is equivalent to the elastic element of the traditional suspension system - spring

when the suspension is in the extension stroke (the piston rod moves downward), the check valve 3 is closed, and the oil in chamber II is compressed, forcing the oil in chamber II to flow to the central chamber through the damping hole 4. The oil flows only through the damping hole, and the flow rate is high, which produces a large damping force, which inhibits the downward movement of the piston rod, so as to quickly attenuate the vibration, which is equivalent to the damping element of the traditional suspension system - the shock absorber

2 establishment of mathematical model of single chamber hydro pneumatic suspension

the following assumptions are followed when establishing the mathematical model:

(1) the fluid flow is steady flow

(2) the influence of temperature change on the system is ignored

(3) the Coulomb friction and viscous friction during movement are ignored

Figure 2 shows the physical model of single chamber hydro pneumatic separated hydro pneumatic suspension

symbols in the figure:

p1, A1 are the pressure of the rodless chamber, the cross-sectional area

v1 are the total volume of the oil in the rodless chamber and the central chamber

p2, A2, V2 are the pressure of the rodless chamber, the cross-sectional area and the total volume

p3, V3 are the gas pressure in the accumulator, the volume

f is the transmission capacity of the suspension cylinder, the tension is positive, the pressure is negative

x is the displacement of the piston rod of the suspension cylinder, and the downward is positive

assume that the suspension cylinder the cylinder is fixed, The piston rod and piston assembly move relative to the cylinder barrel

output force equation:

f=p2a2-p1a1 (1)

total flow through damping hole and check valve:

q=a2 - (2)

dv2= (3)

where: dv2 - volume change of liquid in chamber II in time DT caused by oil compressibility

k - Volume elastic modulus of oil

flow through damping hole:

q1=cda01sign () (1)4)

where: CD -- flow coefficient

a01 -- overflow area of damping hole

sign() = (5)

ρ—— Oil density

flow through the check valve:

q2=cda02sign() (6)

where: A02 - flow area of the check valve

for the gas in the accumulator,

p3v3r = p30v30r (7)

where: P30, V30 initial pressure and volume of the gas in the accumulator

r - gas polytropic index. For ideal gas, r=1 in isothermal process and r=1.4 in adiabatic process. The polytropic index of the actual gas can be taken as 1.7 [4]

v3=v30+ (a1-a2) x in the adiabatic process+ Δ V1+ Δ V2 (8)

where: Δ V1 machine looks elegant, Δ V2 is the volume change of the liquid in the large and small cavities due to oil compression, and there are:

Δ V１＝(9)

Δ V2 = (10)

and for liquids in large and small cavities:

v1=v10+a2x - Δ V1－ Δ V2 (11)

v2=v20 － a2x (12)

where: V10 and V20 are the initial volume of liquid in large and small cavities respectively

for the accumulator outlet:

p3 － P1= ξ Psign (13)

where: ξ—— The pressure loss coefficient

a3 - the sectional area of the oil pipe at the outlet of the accumulator

q3 - the flow through the orifice of the accumulator

q3= (a1-a2) (14)

equations (1) ～ (14) are the nonlinear mathematical model of the oil-gas separation type oil-gas suspension with a single air chamber. It is impossible to obtain the analytical solution of the above nonlinear equations, and only the simulation solution can be used to obtain its numerical solution

3 experimental study on hydro pneumatic suspension with single air chamber

in order to verify the correctness of the above mathematical model, it is necessary to carry out bench test on hydro pneumatic suspension. The test bench principle of suspension can be found in reference 4

the test equipment in this paper is the vehicle road simulation test-bed of the structural vibration fatigue test room of the technology center of Xuzhou Construction Machinery Group Co., Ltd. The whole set of equipment and instruments is a multi axis excitation electro-hydraulic servo test system produced by German karshenk company. This set of equipment can generate sine wave, random wave and other signals of various amplitudes and frequencies in real time as driving signals. The test bench is controlled and recorded by S59 digital control equipment and VAX workstation, which is a high-precision equipment specially for the test and research of hydro pneumatic suspension [5]

the standard sinusoidal signal is used as the excitation signal in the test, and the specific parameters are shown in Table 1. The output signal is recorded through the workstation

4 comparison of test and simulation results

take the hydraulic cylinder parameters as input parameters, and use MATLAB software to simulate. See Table 2 for the selection of parameters in the model

due to space limitations, this paper only gives the comparison diagram of test data and simulation results when frequency f=0.5, 1.67, 5 Hz, amplitude a=20 mm (see Fig. 3, 4, 5)

5 conclusion

(1) the test data of hydro pneumatic spring suspension are basically consistent with the simulation results, which shows that the nonlinear mathematical model of hydro pneumatic spring suspension established is basically correct, and the model can be used to simulate the characteristics of hydro pneumatic suspension

(2) under low-frequency excitation, the test data has obvious mutation at the speed of zero, and the mutation value is about 3000 n, which has obvious error compared with the simulation results. After analysis, the main reason is that the static friction of hydraulic cylinder is not considered in the mathematical model. According to the research of literature 6, the static friction of this typical shock absorber is 500~5000 n. since the hydraulic cylinder used in this test is a new hydraulic cylinder, the static friction value should be large, which can be clearly seen from Figure 3. When high-frequency excitation occurs, the hydraulic cylinder is in a trembling state, and the static friction is very small. At this time, the output force of the hydraulic cylinder is large, and the relative error is small, so there is no obvious sudden change in the figure

(3) there is a certain error in the trend between the simulation characteristic curve and the test data under high-frequency excitation. After analysis, the reason is that the temperature rise of the hydraulic system is not considered in the established mathematical model. However, it can be seen from the comparison chart that the error is small. For general theoretical analysis and engineering applications, the established mathematical model has been able to meet the accuracy requirements

references

1 Wu Renzhi Modeling, simulation and experimental research of hydro pneumatic suspension system dynamics: [doctoral dissertation] Zhejiang University, 2000

2 Zhao Chunming Research on the dynamics theory and related control technology of hydro pneumatic suspension system: [doctoral dissertation] Dalian University of technology, 1998

3 wangguoli et al Current situation and development trend of vehicle active suspension technology Journal of ordnance industry, 2000, (8) supplement

4 scholarly awards Research on vibration damping performance of cxp1032 truck crane hydro pneumatic suspension system: [Master's Thesis] China University of mining and technology, 2000

5 Zhang Yi Mathematical modeling, simulation and experimental research of hydro pneumatic spring suspension: [Master's Thesis] China University of mining and technology, 2003

strive to narrow the gap with developed countries 6 Stefaan W.R duym Simulation Tools modeling and Identification for an automotive Shock Absorber in the Context of Vehicle Dynamics. Vehicle System Dynamics, 33(2000)(end)

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